1. Field of the Invention
The present invention relates to integrated active RC or MOSFET-Channel filters using operational amplifiers. More particularly, the present invention relates to a process independent technique which allows for gain bandwidth product of the operational amplifier to track the resistance and capacitance values.
2. Description of the Related Art
Filter designs in consumer wireless applications come in a few different forms, dependent on frequency. For instance, SAW, dielectric ceramic, and crystal filters are the most commonly used nonlumped element filters. In modern digital communications, the accuracy of the filter frequency characteristics is frequently a prolific source of product failures due to the more stringent requirements placed on their performance.
The most common cause of severe performance degradation that can be attributable to filter performance in digital communication systems is the passband frequency drift with respect to the center frequency of the filter. The passband frequency inaccuracy is usually due to the component production tolerance and thermal characteristics. Most of the digital modulation techniques are sensitive to bandlimiting phenomena. In addition, passband drifting also impairs the group delay budget for the modulation.
Elliptic filters offer the most efficiency in terms of rejection versus filter order. The problem with implementing elliptic filters is that they require precise matching of the phase response of a path comprised of two active integrators with a purely passive path which may be in the form of a feed forward capacitor. The phase errors of the active integrators move the zeros in the stop band portion of the transfer function of the filter which, in turn, causes excess peaking at the edge of the pass band.
Many communication systems, such as baseband IF processors in a cellular telephone, require the use of high order analog continuous time filters. These filters are often integrated as ladder structures which mimic the low pass band sensitivity of RLC prototype passive ladder filters.
Monolithic continuous-time filters are often active RC circuits that include amplifiers, resistors, and capacitors in a feedback configuration. The frequency response of an RC active filter depends on coefficients that are products of absolute resistance and capacitance values, both of which can be subject to considerable random variation with monolithic processing. However, ratios of resistances and ratios of capacitors remain substantially constant with process variations; therefore, ratios of RC products also remain stable.
Active RC filters can provide useful performance up to a few megahertz, but are limited by the performance and bandwidth of amplifiers as well as the parasitic effects mentioned above. Moreover, the amplifiers consume power and limit the dynamic range.
FIG. 1 shows a conventional active RC integrator filter with an operational amplifier 101, a feedback capacitor C.sub.1, an input parasitic capacitance C.sub.in, an input capacitor C.sub.2 and resistor R. The operational amplifier 101 has a gain A(s) of -.omega..sub.u /s where .omega..sub.u is the unity gain frequency of the operational amplifier 101. The transfer characteristic of this active RC integrator filter is shown by the following expression. ##EQU1## Equation (1) can be simplified to the following expression. ##EQU2## Which can be alternatively expressed as the following. ##EQU3## A reasonable assumption for practical applications is that the integrator unity gain frequency bandwidth will be much smaller than the operational amplifier unity gain bandwidth. Therefore, equation (3) can be simplified to the following expression: ##EQU4## If the input capacitor C.sub.2 of the filter is zero, thereby displaying low pass filter characteristics, it can be shown from the above equation (4) that a non-dominant pole .omega..sub.non-dominant is located at a frequency defined by the following expression: ##EQU5##
FIG. 2 shows a bode plot of the transfer function for the active RC filter shown in FIG. 1 displaying low pass characteristics, i.e., where capacitor C.sub.2 is zero. It can be seen from FIG. 2 that the active RC integrator filter has the unity gain product 1/RC.sub.1 at frequency f1 and the first non-dominant pole 202 at frequency f2.
FIG. 3 illustrates passband peaking of the conventional active RC integrator filter as shown in FIG. 1. The ideal filter characteristic 301 illustrates the effect of a transfer function zero located at an ideal zero frequency 303. By contrast, an actual conventional active RC integrator filter characteristic shows the passband peaking at a peaking frequency 305 whose transfer function zero is located at zero frequency 304. From FIG. 3, it can be seen that the zero frequency of a conventional filter 304 is shifted from ideal zero frequency 303. This is due to the phase shift of the operational amplifier in the integrator filter. In turn, due to the transfer function zero shifting from ideal frequency 303 to the conventional filter transfer function zero frequency 304, the conventional filter exhibits pass band edge peaking 305.
For example, in a code division multiple access (CDMA) baseband filter, the excess phase can be determined by the following expression. ##EQU6## With the CDMA baseband filter having the unity gain bandwidth 1/RC.sub.1 of 2.pi.*660 kHz, the gain bandwidth product .omega..sub.u at 2.pi.40 MHz, and the values of the feedback capacitance C.sub.1 and the input parasitic capacitance C.sub.in of 8 and 0.7 picoFarads (pF), respectively, the excess phase according to the above expression is 1.03.degree.. This excess phase, in turn, results in 2 dB of baseband edge peaking in an all pole ladder filter structure.
In ladder implementations of elliptic filters with resonant transmission zeros, the above result is worsened since the input capacitance C.sub.2 is finite, resulting in a zero. Using the same values for the unity gain bandwidth 1/RC.sub.1, input capacitance C.sub.2, feedback capacitance C.sub.1, and input parasitic capacitance C.sub.in, and the gain bandwidth product .omega..sub.u, the excess phase according to equation (6) is 1.5.degree.. This excess phase cause approximately 3 dB of baseband edge peaking in the elliptic CDMA filters.
The results above illustrate that even a single degree of excess phase for these filters as used in the communication channels, for example, in cellular phones, is sufficient to cause approximately 1 dB of peaking at the passband edge of the filter distorting the filter characteristics.
Therefore, there exists a need for filters generally, and, in particular, for continuous time applications, which can effectively cancel excess phase errors to minimize undesirable passband edge peaking.